Asymptotic theory of 3D thermoelastic stress analysis of honeycomb sandwich panels with composite facesheets

Abstract

This work presents an asymptotical thermoelastic model for analyzing symmetric composite sandwich plate structures. Use of three-dimensional finite elements to analyze real-life composite sandwich structures is computationally prohibitive, while use of two-dimensional finite element cannot accurately predict the transverse stresses and three-dimensional displacements. Endeavoring to fill this gap, the present theory is developed based on the variational asymptotic method. The unique features of this work are the identification and utilization of small parameters characterizing the geometry and material stiffness coefficients of sandwich structural panels in addition to the small parameters pertaining to any plate-like structure. In this formulation, using variational asymptotic method, the three-dimensional thermoelastic problem is mathematically split into a one-dimensional through-the-thickness analysis, and a two-dimensional reference surface analysis. The through-the-thickness analysis provides the constitutive relation between the generalized two-dimensional strains, and the generalized force resultants for the plate analysis, it also provides a set of closed-form solutions to express the three-dimensional responses in terms of two-dimensional variables, which are determined by solving the equilibrium equations of the plate reference surface. Numerical results are illustrated for a typical composite sandwich panel subjected to a linear-bisinusoidal thermal loading. The three-dimensional responses of the composite sandwich structure from the present theory are compared with the three-dimensional finite element solutions of MSC NASTRAN®. The results from the present theory agree closely with three-dimensional finite element results and yet enable order of magnitude saving in computational resources and time.